Gravitational Field

Field of force due to point mass

Library

Forces and Torques

Description

This block represents the gravitational field of a point mass.
This field applies a gravitational force at the center of mass of
each rigid body. The force magnitude decays with the square distance
from the field origin, coincident with the base port frame origin.
The force on a rigid body follows from Newton's universal gravitation
law:

Fg=−GMmRBF2,

where:

Fg is the
force that the gravitational field exerts on a given rigid body.

G is the universal gravitational
constant, 6.67384 × 10-11 m3kg-1s-2.

M is the total mass generating
the gravitational field.

m is the total mass of the rigid
body the gravitational force acts upon.

RBF is the
distance between the source mass position and the rigid body center
of mass.

The figure shows these variables. The plot shows the
inverse square dependence between the gravitational force and distance.

The source mass can be positive or negative. Combine multiple
instances of this block to model the gravitational effects that positive
and negative mass disturbances impose on a stronger gravitational
field, such as a reduction in the gravitational pull of a planet due
to a concentration of low-density material along a portion of its
surface.

This block excludes the gravitational forces that other rigid
bodies exert on the field source mass. To include these forces, you
can connect Gravitational Field blocks to other rigid bodies in the
model. Alternatively, you can use the Inverse Square Law Force block
to model the gravitational forces between a single pair of rigid bodies.

The gravitational field is time invariant. To specify a time-varying,
spatially uniform field, use the Mechanism Configuration block.

Dialog Box and Parameters

Mass

Total mass generating the gravitational field. The resulting
gravitational forces are directly proportional to this mass. This
mass adds no inertia to the model. The default value for the mass
parameter is 1.0 kg.

Ports

Frame port B represents a frame with origin at the point mass
responsible for the gravitational field.